Abstract
Supersaturated design (SSD) has received much interest because of its potential in factor screening experiments. Recently, Chen and Liu [Chen, J., Liu, M.Q., 2008a. Optimal mixed-level k -circulant supersaturated designs. J. Statist. Plann. Inference 138, 4151–4157] explored the construction of E ( f NOD ) -optimal mixed-level SSDs using k -cyclic generators. As an extension, this paper further studies how to construct optimal mixed-level k -circulant SSDs under the χ 2 ( D ) criterion. A sufficient condition under which the generator vector produces a χ 2 ( D ) -optimal SSD is obtained, and some other properties of the resulting SSDs are investigated. Note that, the construction of optimal mixed-level k -circulant SSDs under the χ 2 ( D ) criterion is much more complicated than that under E ( f NOD ) . Hence, an algorithm for finding generators of (nearly) χ 2 ( D ) -optimal designs is provided, and many (nearly) χ 2 ( D ) -optimal mixed-level SSDs are then constructed.
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